I must say that this puzzle has beaten me down. 2 hours of thinking it over has gotten me nowhere, so I humbly come before you all to ask for a life preserver . Could you help me understand what I've done wrong or what the next steps might be? I do believe that all of these puzzles must have a solution, but I'm afraid that I'm missing some technique that would be valuable for puzzles like this one.

You were right with the clues you had. At this point you'd have to do a process of elimination. There are only two possible answers for 1950 (8.5 and 8.9). If you choose 8.5 you won't be able to solve clue number 6, which says that 49 seconds comes 6 years before 84 seconds.

You should NEVER need to do “what if”. You deduced that the 9.0 was the 84 second quake from clues 4 & 6 and that was very good, IMHO. The next domino was lying right next to that one. You can see that 49 seconds and 84 seconds are down to only two possibilities each as far as year goes, and since they’re tied together by clue 6 ONE OF THEM HAS TO HAVE HAPPENED IN 1956! That means that 41 seconds and 99 seconds can be crossed off as candidates for 1956. As you comb back through the clues, you can see that eliminating 1956 as a possibility for 41 seconds, eliminated 1950 as a possibility for 8.5, leaving only 8.9 for 1950. The rest topples like a house of cards. The technique that makes this possible is shown in this video…

You already had 9.0 with 84 seconds. The logic comes from clues 4 and 6. From 4 you know that 49 seconds is 6 years before 9.0. From 6 you know that 49 seconds is 6 years before 84 seconds. So 9.0 is also 84 seconds. The other clues just fall into place.

But let me know if it's correct. Sometimes it looks good but not right.

Thanks for the quick responses, and especially to you Laura for solving it. I am ASSUMING that it is correct because with that in place I was able to come to the same conclusion. Unfortunately, I moved on as I was logged off and searching for games < 25% success rate. However, it does beg the question: how did you format my picture in order to appear nearly identical to the solution? That's pretty impressive in it's own right!

Believe it or not, I just took your image and modified it with the simple Windows Paint accessory . I didn't bother with PhotoShop or Illustrator because with Paint I was able to copy and drag the green zeros and red exes to the various locations on the grid without having to deal with layers. It does get a little sloppy but it's quick.